This journal, which is published only in electronic form, aims to enhance mathematics teaching for all ages (and abilities) up to 18 years, through relevant articles, reviews and information from around the world.
It is aimed at practitioners and educationalists, providing a medium for stimulating and challenging ideas, offering innovation and practice in all aspects of mathematics teaching and learning.

Anyone involved in the teaching of mathematics is welcome to contribute.
Intending contributors are advised to read Notes for Contributors.About the IJMTL gives details of the editorial team and publishing policy.

Articles published to dateSizes of files are given in[kb]as a guide to downloading times.

This study aims to explore undergraduate students’ ways of thinking while solving problems in the abstract mode about linearly independent/dependent vectors. It also focuses on what students understood about linear independence/dependence concepts. The study was conducted with 186 mathematics teacher-candidates. The responses of these students to four problems and interview data conducted with eight students were used to identify a student’s way of thinking.

This study focuses on students in first year environmental science degree programs, where traditionally mathematical emphasis has been much less than within the strict science or math majors. The authors attempt to gain insight into why many students fail mathematical courses even when the mathematical requirements are not as demanding.

This paper uses a series of models to illustrate one of the fundamental processes of model building – that of enrichment and elaboration. The paper describes how a problem context is given which allows a series of models to be developed from a simple initial model using a queuing theory framework.

This article examines prospective elementary teachers’ conceptions of unitizing with whole numbers and fraction concepts and operations throughout a semester-long mathematics content course. The results indicate that the prospective teachers were successful with iterating units and developing composite units within both whole numbers and fractions.

This article examines how secondary school students think about functional relationships. More specifically, seven students’ intuitive knowledge in regards to representing two real-world situations with functions was examined. We found students do not tend to represent functional relationships with coordinate graphs even though they are able to do so, instead representing the physical characteristics of the situation

This paper explores the relationship between social backgrounds and geographical locations with mathematical achievement. Using the national testing system in Australia, correlations between the variables were explored and it was found that students from rural and low SES backgrounds are still being marginalised in school mathematics – in terms of their success.

This study comes at an opportune moment for Japanese and U.S. educators, policymakers, and researchers given the trends of global policy and equity-based reform. Discussions of academic achievement in both societies allows us to examine mathematics education as a public good versus private commodity in order to best serve the needs of students. Research was conducted as a visiting scholar at the University of Tokyo, and supported by classroom experience in four public and private schools.

This article addresses issues in equitable and quality STEM education, and comes at a significant time as students, educators, and policymakers strive to meet federal and state standards such as the Mathematics Common Core State Standards (CCSS) and Next Generation Science Standards (NGSS).

This article presents and discusses an example of how teachers’ discussions of mathematical knowledge for teaching (MKT) items elicited their beliefs about the knowledge needed to teach mathematics. One category of MKT is “horizon content knowledge,” and this can be described as mathematical knowledge not directly deployed in instruction — or knowledge behind as well as ahead of the pupils in an actual teaching situation.

This paper examines the effects of using music-themed activities in mathematics lessons on two groups of participating students’ mathematics achievement and dispositions, including beliefs about success, attitude, confidence, motivation, and usefulness, using a pre/post test method.

This research focused on mathematics pre-service teachers’ understandings of linear and quadratic inequalities to determine whether they possess common misconceptions and difficulties with inequalities. Results provided evidence that many pre-service teachers have misconceptions and difficulties that cause them to misunderstand inequalities.

This paper explores students’ personal meaning and interpretation of the vertex of a quadratic function in relation to their understanding of quadratic functions in two different representations, algebraic and word problem. Several categories emerged from students’ personal meaning of the vertex including vertex as maximum or minimum, vertex in relation to symmetry, vertex as a starting point or turning point, vertex as an intercept, vertex as an intersection, and miscellaneous.

Much research has been conducted on how elementary students develop mathematical understanding and subsequently how teachers might use this information. This article builds on this type of work by investigating how one high-school algebra teacher designs and conducts a lesson on exponential functions. Through a lesson study format she studies with her colleagues how other algebra students have mathematically modeled a bacteria growth problem with no prior formal instruction.

Mathematics educators have had a long standing interest in students’ understanding of decimal numbers. Most studies of students’ understanding of decimals have been conducted within Western cultural settings. The present study sought to gain insight into Chinese Hong Kong students’ and regional Australian students’ general performance on a variety of decimals tasks and to investigate students’ error patterns.

Students start to memorize arithmetic facts from early elementary school mathematics activities. Their fluency or lack of fluency with these facts could affect their efforts as they carry out mental calculations as adults. This study investigated participants’ levels of brain activation and possible reasons for these levels as they solved arithmetic exercises mentally.

The purpose of this study was to deconstruct the relationship between visual static models and students’ written solutions to fraction problems using a large sample of students’ solutions. Students’ written responses to open-ended tasks were examined to determine common solutions and errors when using visual static models.

This qualitative study examined middle school students’ performance, solution strategies, difficulties and the underlying reasons for their difficulties in calculating the volume of a rectangular prism. The data was collected from 35 middle school students (6th, 7th and 8th grade students) enrolled in a private school in Istanbul, Turkey.

Professional development (PD) programs often evaluate their impact on teachers’ learning by assessing teachers either individually or in groups. The goal of this paper is to illustrate the variety of paths teachers might follow as a result of working in groups within online PD settings. Data are drawn from a PD program for grades 5-9 mathematics teachers.

Mathematics textbooks are a predominant resource in primary school in Greece, as well as in many other countries. The present study reports on both a content analysis of Greek mathematics textbooks with regard to the types of word problems represented in them and a quantitative analysis of children’s achievement in these problems.

This study investigates the scenes behind Chinese pre-school children's mathematics performance using teacher questionnaires and interviews. Results indicated that the Chinese number system appeared to afford advantages to Chinese children in learning individual mathematics concepts but this was not enough to explain why children perform well in other areas.

The present study examined the structure of elementary pre-service teachers’ mathematics anxiety and mathematics teaching anxiety by asking whether the two systems of anxiety are related. The Turkish Mathematics Anxiety Rating Scale Short Version and the Mathematics Teaching Anxiety Scale were administered to 260 elementary pre-service teachers. Results of the study revealed that overall pre-service teachers’ had a low-level of mathematics anxiety and mathematics teaching anxiety.

The aim of this study is to examine the effects of engaging prospective mathematics teachers in peer assessment, both as assessors and assessees, on the development of their assessment skills in general and assessment of geometrical proofs in particular. The research was conducted within a Method course in which peer assessment activities were employed.

This study examined students’ processes in their generation of symbolic and graphic representations of given polynomial functions. The purpose was to investigate how students perform these translations. The result of the study suggests that students of different ability levels process translations differently and that students’ apparent difficulties with translations may be directly connected with their processes and obstacles encountered during translations.

This paper examines how mathematical understandings might emerge through student-centred inquiry. Data is drawn from a research project, conducted in three New Zealand primary schools, on student-centred curriculum integration that situated mathematics within authentic problem-solving contexts and involved students in collaboratively constructed curriculum.

An innovative task used in teacher education – Lesson Play – that involves presenting a lesson in the form of an interaction between a teacher and students is explored. The paper examines the motivation for the development of this task and, through specific examples, describes the iterative design process in which the task was refined and improved. The authors demonstrate how the task, initially designed considering mathematics, can be adapted and extended for different content areas.

Over the past decade it has been frequently reported that East Asian students are outperforming their Western counterparts in international tests of mathematics at middle-school level. This paper probes classroom discourse in an attempt to shed some light on the reasons for this phenomenon.

The goal of this article is to provide teachers with an alternative perspective in writing multiple-choice questions. To the techniques and advice available in the literature on the topic, three further aspects are added whose provenance is an emerging line of research – the exemplification of concepts. The objective is to expand multiple-choice questions from their present almost exclusive function of evaluation, and turn them also into a useful instrument for everyday classroom work.

Research has shown students can identify practices considered appropriate for achieving when learning mathematics. However, an individual’s espoused theory (what is said) does not necessarily match their theory-in-use (what is done). Further investigation into students’ beliefs and actions are required to explain the difference between what they say and what they do. This article presents the espoused theory, theory-in-use and the follow-up discussion of three underachieving students where the identified differences were explored.

This study examines the results of a three-site administration of the Learning Math for Teaching instrument, a multiple-choice instrument designed to measure aspects of Mathematical Knowledge for Teaching. Results indicate that Math Teachers’ Circles are impacting teachers’ performance on the Number Concept and Operation subsection, leading to implications for future research.

This paper reflects on a case study of a Grade one teacher to illustrate how she uses multiple representations as a learning progression for the purposes of abstraction. A detailed description of one specific lesson is provided in which multiple representations are incorporated and also analyses her pedagogy with her four chosen representation forms.

This paper summarises the current peer-reviewed literature of the research into the mathematical content knowledge of pre-service elementary teachers. The need for further research in this area is identified.

This article explores the mathematical content knowledge of one entire cohort of pre-service teachers through analysing their performance in a Secondary Mathematics Audit that was developed for the International Comparative Studies in Mathematics Teacher Training that was initiated by the University of Plymouth. We study how their mathematical content knowledge evolved during their one-year postgraduate teacher education programme by using a pre and post-course test scheme.

This is an ethnographic study of promotion of metacognition, focusing on the teaching practices in secondary mathematics classrooms of three teachers in the UK. Observations of their teaching and interviews regarding their teaching were conducted. The main aim was analysing and substantiating the parallels and differences among the teaching practices, providing an account of the patterns in the teachers’ promotion of metacognition and the underpinning factors.

This article reports an innovative use of photographs in a pencil-and-paper test which was developed to assess young children’s understanding of mass measurement. 295 tests were administered by 13 teachers of Years 1 and 2 children in 3 urban and rural schools with the aim of more closely connecting written assessment with classroom experiences of young children.

This paper presents a framework used to analyze the extent to which assessments accompanying three published elementary grades 3-5 curricula in the United States provide students with opportunities to engage with key mathematical processes. The framework uses indicators for five criteria to assess the processes of reasoning, communication, connections, and representation.

This study explores the effects of providing ninth-grade students with the chance to take part in decision making concerning the mathematics level they would be assigned to in high school. Decisions concerned their self-competence regarding their mathematical abilities, their learning goals and the class atmosphere.

This article explores junior high school students’ views regarding what it takes to be successful in mathematics. Qualitative and quantitative methods were employed to collect and analyse data, describe and interpret junior high school students (12-14 years) perceptions about what it takes to be successful in mathematics.

This qualitative study illustrates how one high school mathematics teacher engaged his students in classroom discourse and promoted in them the use of appropriate mathematics language to communicate their thinking and make sense of mathematics concepts. The study also shares students’ perceptions of the teaching approach.

This paper adds to a discussion initiated by Askew (2007) about two contrasting views of scaffolding; as a ‘tool for results’ and a ‘tool-and-result’. The wider study the article is drawn from took place in four primary classrooms with Pasifika students within a low socioeconomic setting.

Statistical power analysis determines the ability of a study to detect a meaningful effect size, where the effect size is the difference between the hypothesized value of the population parameter under the null hypothesis and the true value when the null hypothesis turns out to be false. Although power is an important concept it is a topic not often covered in any depth in a basic statistics class and it is often ignored by practitioners.

This paper examines the role of Professional Development as a support mechanism for mathematics teachers in low socio-economic schools and reports on the results of implementing a peer mentoring model with teachers in schools of this type.

The main aim of this paper is to report on an investigation into primary pre-service and in-service teachers’ content knowledge of decimals. The participants were asked to complete four decimal tasks including the ordering of decimals, operating with decimals and converting a fraction to a decimal. The findings indicated a reliance on formal procedures and that incorrect responses indicated a fundamental lack of understanding of place value.

This paper focuses on how pedagogical reform in Australia has resulted in a reduced emphasis on the teaching of computational algorithms and led to a diversity of alternative mechanisms to teach students whole number computations. A study is conducted into the current methods used by students in completing written computational tasks.

The purpose of the present study was to investigate the role of various aspects of apprehension (perceptual, operative and discursive) in geometrical figure understanding and the respective students’ self-beliefs about using representations as a useful tool for understanding geometrical concepts and for solving geometrical tasks.

Moving from primary school (Year 6) to the next stage in schooling (Year 7 intermediate or middle school) can provide challenges for students, teachers, and parents. This paper examines the findings of a study carried out to investigate these challenges with a focus on mathematics for 65 students from six different urban primary schools in New Zealand.

In this paper, the design of an online resource, Equations2go, for helping students learn to solve linear equations is investigated. Students learning to solve equations need to consider their overall strategy as well as the procedures for each step. Students were encouraged to develop strategies for solving equations with interactive software, Equations2go, which allowed students to decide on strategies while the computer carried out the procedures.

This paper examines the reasons that Chinese students, mainly using procedural methods including rote learning and memorisation, usually out perform Western students who are encourage in their learning to construct a conceptual understanding of the mathematics they learn.

This paper introduces a new approach to compute the partial fraction decompositions of rational functions and describe the results of its trials at three secondary schools in Hong Kong. The responses from the teachers and students concerned indicate this new approach has potential to be introduced at the senior secondary level, as an alternative to the method of undetermined coefficients described in common secondary mathematics textbooks.

This article describes a professional development initiative for fifteen mathematics teachers in the use of dynamic geometry software GeoGebra. Teachers’ impressions and beliefs concerning both the training and the software were researched in the context of applicability in Nepalese schools.

The cognitive purpose of the paper is to show how to generalize the process of determining image characteristics by using a lens equation converted to an algebraic function. Its far-reaching goal is to ignite learners’ curiosity of interpreting natural phenomena through employing more extensive mathematical embodiments.

The purpose of this qualitative research is to examine the views of 21 secondary mathematics student teachers attending Mathematical Modelling Course regarding mathematical modelling in a state university in Turkey; reasons why they chose this course and their expectations from the course in question.

This study analyzed the representation of number sense and its connection to other mathematics concepts in both traditional and reformed first-grade textbooks in China and the United States, and explored the learning opportunities that the textbooks in each country provide for their children in developing number sense.

Using a large dataset from a study related to online professional development for eighth grade teachers of mathematics, the paper provides a snapshot of the current state of teachers’ knowledge related to proportional reasoning and functions. The paper also considers how teachers’ knowledge is related to student knowledge in these two areas.

This study investigated the development of the concept of variables in middle grades mathematics textbooks during four eras of mathematics education in the United States. Findings revealed that each of the middle grades mathematics curricula examined used variables, but in varied proportions and levels of complexity. There were also some noticeable changes in the treatment of variable ideas found in the curriculum selected for the present NCTM era when compared with the treatment in the other three curricula.

Parental involvement in the form of ‘at-home’ interest and support has a major influence on pupils’ educational outcomes and attitudes. Many parents, however, feel uninformed about current educational practices and how they can be more involved with their child’s learning. This article provides some examples of mathematics education projects, initiatives and interventions as documented in the literature, as a context for discussing in detail two initiatives undertaken with the parents of two Australian schools.

This research provides insight into one US state’s effort to incorporate higher-order thinking on its Algebra I End-of-Course tests. To facilitate the inclusion of higher-order thinking, the state used Dimensions of Thinking and Bloom’s Taxonomy. An analysis of Algebra I test items found that the state’s initial interpretation and application of Dimensions of Thinking and Bloom’s Taxonomy was faulty and inconsistent; as a result, few Algebra I test items from 1998 and 2001 were found to assess higher-order thinking

This study investigated and compared the geometry knowledge and levels of pre-service elementary teachers from the United States and Taiwan. Forty pre-service teachers in Taiwan and 48 pre-service teachers in the United States at the beginning of their teacher education programs completed the Entering Geometry Test (EGT) and the van Hiele Geometry Test (VHGT) developed by Usiskin (1982).

This longitudinal study analyzes middle school mathematics pre-service teachers’ development of teaching goals. The Teaching Goals Inventory (TGI) (Angelo & Cross, 1993) was administered on four occasions. The participants were part of a teacher preparation and master’s degree program.

The article aims to present findings of a study on the profile of traditional/constructivist beliefs of mathematics teachers in Latvia connected with effective teaching. Latvian mathematics teachers’ beliefs about effective teaching tended towards constructivism, though in response to many questions traditional standpoints still remained.

The purpose of this study was to investigate the effect of instruction in alternative solutions on Taiwanese eighth-grade students’ mathematical problem solving performance. This study was exploratory rather than experimental. Alternative-Solution Worksheet (ASW) was developed to encourage students’ engagement with alternative solutions to mathematical problems during instruction.

The ability to decode graphics is an increasingly important component of mathematics assessment and curricula. This study examined 50, 9 to 10-year-old students, as they solved items from six distinct graphical languages that are commonly used to convey mathematical information.

This study examined four Romanian first grade teachers’ knowledge about place value concepts, and the relationship between this knowledge and their classroom practice. Findings reveal a direct relationship between teachers’ content and pedagogical content knowledge and their student learning of place value concepts.

This paper discusses teacher beliefs and instructional practices, investigates why some translations seem to be more difficult than others and provides instructional recommendations to assist students and teachers with mathematical translations.

This study investigates to what extent arithmetic ability and self-regulated learning skills in the beginning of lower secondary school predicts measures of students’ performance in mathematics at the end of lower secondary school. Arithmetic ability and self-regulated learning skills were tested in the first two weeks in lower secondary school. Post-tests were performed the last two months in lower secondary school.

This paper explores the relationship between language and developmental processes of logical tools through the analysis at different levels of some ‘linguistic-manipulative’ activities in a primary school classroom.

This study investigated the effects of modes of personalisation of instruction crossed with two levels each of verbal ability and cognitive style as moderator variables on the mathematical word problems achievement of 450 junior secondary Nigerian students.

In this paper, pre-service mathematics teachers were presented with examples in Use of Computers in Mathematics Education (UCME) course on how to use computer technology in mathematics education and how mathematical relationships are investigated. This paper attempts to reveal the mathematical thinking processes and experiences lived by pre-service teachers in the course of investigation and discovery processes.

This paper presents the results of a study focused on the issue of how proctored testing affects the learning outcomes and integrity in an Intermediate Algebra course setting. The study follows a model of assessment where students in one group have taken two of their five unit exams as proctored tests along with a proctored Comprehensive Final Exam, compared to a second group who take all unit tests online, but who do complete a proctored Comprehensive Final Exam.

The mathematics education community recognizes the integrality of reading and writing in learning and communicating mathematics knowledge. This paper explores the integrality of reading and writing in mathematics and outlines techniques that can be utilized in mathematics assessment to create experiences that promote reading and writing as tools for articulating mathematics understanding.

The article discusses using differentiated instruction in mathematics education for pre-service teachers, including background information and details on a differentiated unit on fractions and integers. In addition, a study was conducted on this lesson and results are included which suggest that students who received the differentiated lesson did better than those students who received a more typical lesson.

The purpose of this study was to examine the relation between the attitudes and components of attitude of the students towards algebra with their algebra achievements. The population for this study consists of all government tenth grade students and their mathematics teachers in Addis Ababa city administration.

The aim of this paper is to investigate the ways in which the number line can function in solving mathematical tasks by first graders (6 year olds). The main research question was whether the number line functioned as an auxiliary means or as an obstacle for these students.

This research article is part of a larger study that examines an initiative to expand teacher expertise in facilitating mathematical problem solving within the framework of developing and field-testing pedagogical resources. We focus on one year of the study and report on the complex process of professional development as teachers move from traditional pedagogies of teacher explanation of mathematical operations followed by student practice to a pedagogy of teacher and student exploration of number operations within a problem-solving environment.

Whether they are acknowledged or not, resources such as textbooks, curriculum guides, assessments, and professional development programs present messages about what is most important for students to learn and how students can best learn this. At times teachers feel obligated to enact these messages, but at other times they feel free to ignore these messages. When do teachers feel obligated to follow messages that they interpret from resources and when do they feel that they can ignore these messages?

A lack of mathematical ability has been identified as a factor resulting in non-completion of courses in Higher Education Institutions. This study investigates how students become involved in mathematics development services/centres and how such services impact on their learning experience. Subsequently, the study presents informative findings and results from a recently conducted survey of the perceptions of Aston University students on the mathematics learning development centre.

This article discusses an open-ended problem involving quadrilaterals that is continually used each semester. The task has been posed to undergraduate and graduate students in methods and problem solving classes. The task involves drawing all possible four sided figures with corners at the dots. A four by four array of dots is included in the instructions and students are asked to develop a system for knowing when they have identified all the quadrilaterals.

This paper presents aspects of mathematics vocabulary and its impact on mathematical comprehension and performance based on representative vocabulary from standardized examinations. Direct and indirect instructional methods for math vocabulary are discussed. Instructional strategies for fostering vocabulary development are also provided.

Five elementary and special education preservice teachers were the focus of this study. Analysis showed that preservice teachers demonstrated different levels of mathematical understanding. The nature of the mathematical tasks they completed in class provided contexts for their developing understanding.

The purpose of this study was to examine whether there is an association between middle school students’ achievement level on standardized test, their ability to recognize structurally the same relationship presented in different modes and their ability to solve problems involving linear relationship with one unknown posed in different modalities.

Many educators believe that mathematical investigation involves both problem posing and problem solving, but some teachers have taught their students to investigate during problem solving. The confusion about the relationship between investigation and problem solving may affect how teachers teach their students and how researchers conduct their research. Therefore, this article seeks to address these issues by first distinguishing between investigation as a task, a process and an activity; and then providing an alternative characterisation of the process of investigation.

Superitem test based on the SOLO model (Structure of the Observing Learning Outcome) has become a powerful alternative assessment tool for monitoring the growth of students' cognitive ability in solving mathematics problems. This article focused on developing a superitem test to assess students' algebraic solving ability through interview method. The findings provided evidence on the significance of superitem test in assessing algebraic solving ability.

This paper reports on the selection and choice criteria for mathematics tasks that are used in an elementary pre-service program. The tasks can be seen as experiential therapy. It can be argued that for teachers to see mathematics, and consequently mathematics teaching and learning, in new ways then they need to personally experience mathematics in new ways. The findings show that teachers’ engagement with such tasks may help them become better positioned to teach mathematics in what are referred to as “warm” ways.

This paper describes the prevailing academic scenarios of a representative group of secondary schools in Assam (India) with special references to students' performance in general and mathematics performance in particular.

In this paper, a Hong Kong primary school lesson on area and perimeter is analysed with a perspective to discuss the meaning for students to have rich mathematical experiences and how pre-designed pedagogical tools could enrich mathematics classroom learning environment which promote re-shaping, shaping and even creation of mathematical knowledge.

The purpose of this study was to examine how geometric concepts are presented in the Turkish elementary mathematics curriculum and in the textbooks in terms of sizes and orientations. For this purpose, the elementary school mathematics curriculum and two sets of textbook series were examined.

This paper describes an intervention at the 8th grade level where university mathematics researchers presented a series of lessons on introductory concepts in probability and statistics. Pre- and post-tests, and interviews were conducted to examine whether or not students at this grade level can understand these concepts.

A solution to the Rubik’s Cube was introduced to an eighth grade mathematics class. The purpose of this study was to determine if an introduction to a solution to the Rubik’s Cube could enhance students’ problem-solving abilities, increase their general interest in mathematics, and enhance students’ problem solving self-efficacy.

The purpose of this paper is to explore difficulties faced by 56 Secondary students when solving problems. The difficulties experienced by students who were prevented from obtaining a correct solution were: (a) lack of comprehension of the problem posed, (b) lack of strategy knowledge, (c) inability to translate the problem into mathematical form, and (d) inability to use the correct mathematics.

This study used concept maps to investigate the effect of using graphing calculators on students' understanding of the derivative at a point. The study looked for differences between the concept images that are held by students' who are using graphing calculators and the students who are not using them.

This manuscript describes a group of middle school age students' exploration of virtual mathematics manipulatives and the authors' professional development process. In the manuscript, the authors share the experiences they had with middle school students and the process that they, as mathematics teachers, used to refine their own learning and teaching alongside the middle school students.

In this paper, we present the results of a survey-based study of the perspectives of mathematics teacher educators in the United States regarding the effects of the conceptual/procedural balance upon four concerns: the type of mathematics that should be learned in school, preservice teacher preparation, instructional conceptualization and design, and assessment.

Effects of a practicum-based elementary mathematics methods course on the beliefs of preservice teachers regarding conceptual knowledge in school mathematics were explored using a pre-post design. The intensity of those beliefs was assessed before and after the methods course using the IMAP Web-Based Beliefs Survey, an instrument constructed by the “Integrating Mathematics and Pedagogy” (IMAP) research group at San Diego State University.

This article attempts to answer the question “What is good college mathematics teaching?” by examining three sources of information: research, student course evaluations, and responses on the website RateMyProfessors.com.

The TIMSS 1999 Video Study revealed that Japan had the lowest (of the seven participating countries) amount of real-life connections in the eighth grade mathematics classrooms, whereas the Netherlands had the highest amount of connections with real life. This article examines more closely how these ideas were actually implemented by teachers in these two countries.

This paper focuses on an open-ended problem. The problem comprises a group of four numbers from which the students are asked to find the one that does not belong. Each of the numbers can be selected as not belonging, each one for different reasons. The problem was given to 164 fifth-grade students. The paper suggests tools for teachers to analyze and evaluate the work of their students when dealing with problems of this kind.

The purpose of this study was to investigate the relationship between learning and instruction in mathematics achievement of 12-year-old students in Saigon, Vietnam. The researcher examined several instructional practices and employed variance estimation procedures for complex sampling designs.

The purpose of this paper is to report a study that explores the thinking strategies of Lebanese grade 7 students in solving a problem involving simple geometric objects and first-degree equations, prior to formal instruction in algebra.

With the recognition of the significant role played by the NCTM Standards and the Principles and Standards within the history of mathematics education within the United States and internationally, it is necessary to consider the philosophical composition of this movement and address specific questions which naturally arise. Eclipsed by discussions of curricular content, philosophical concerns are often absent from contemporary discussions of mathematics education reform efforts.

Today, research often considers the content and pedagogy associated with the NCTM Principles and Standards for School Mathematics (NCTM, 2000). However, philosophic analysis of NCTM’s position remains only infrequently investigated. This paper investigates the Principles and Standards from an aesthetic perspective, asking the question, “What does NCTM believe to be ‘Beautiful Mathematics?’”

This study examines the actual conditions of instruction provided by Korean mathematics teachers while adjusting the curriculum with respect to the consideration given to the needs of individual students and regional specialization in their class.

The concept of equality and the equal symbol is discussed in this paper. Based on an instrument derived from previous research results, a study of how fifth and sixth graders understand the concept of equality was conducted and a subsequent analysis was accomplished

This paper seeks to provide further evidence of the problems graduate students face as they are teaching. In order to accomplish this, this study presents a singular case study of the graduate teaching instructor of Mr. M culled from an on-going investigation of the struggles graduate teaching assistants face when front-line instructors.

In this paper we propose a new thinking strategy directed to improve the mathematical problem–formulating process. Several specific strategies proposed by many authors are seen as techniques, related to the implementation of our strategy. The results have been applied in the Cuban mathematics teachers' training.

This study tries to analyse the performances of students and explore the mistakes made by the students taking a Calculus course when they are finding solution sets for inequalities. To these purposes, an examination was given to science students who have taken a calculus course at a Turkish University.

This discussion paper looks into the teaching of statistics in primary and secondary schools. It forms part of a joint study by the International Commission on Mathematical Instruction and the International Association for Statistical Education entitled Statistics Education in School Mathematics: Challenges for Teaching and Teacher Education.

This paper presents the findings of a pilot evaluation funded by the Belfast Education and Library Board of the Cognitive Acceleration in Mathematics Education Programme in a number of post-primary schools in Northern Ireland. It looks at the impact of the programme on teachers’ classroom practice and teaching methods and its use as a professional development tool.

This paper describes the results of a pilot study designed to investigate differences in mathematical self-efficacy for two groups of students taking a general mathematics unit as part of their year 1 computing and IT undergraduate studies.

This paper addresses matters of general significance to mathematics education but it does so in the context of recent developments in England. In particular, the reader is assumed to be loosely familiar with the Frameworks (also sometimes referred to as the Strategies) for Key Stages 1 and 2 (ages 5-11) and for Key Stage 3 (ages 11-14).

This study examined the effect of the use of graphing calculators on students' understanding of the concept of the derivative at a point. It investigated whether or not the graphing calculator with its visual representation helps students construct an appropriate concept image of the derivative at a point.

This study investigates whether computer support has a contribution to make in teaching by the limit concept. After splitting 52 students into two groups, the limit concept was instructed by using classical methods to one of the groups whereas using computer support was employed in the other group.

The purpose of this study is to investigate the impact of using Trigonometric Graphs, a teacher created web-based simulation, and asynchronous online discussion on students understanding of and performance in sketching transformation of trigonometric curves.

The purpose of this paper is to discuss the current reform in the Turkish Mathematics Education at the elementary level by summarizing the types of program development models and changes involved in the current reform.

In this paper, the writer looks at how the results of elections can vary greatly depending on the voting method used and how the most popular candidate is not always the one elected. A new proof of Arrow's impossibility theorem is presented as well.

In this paper, two special graphical representations of mathematical networks, mind maps and concept maps, are presented. Both knowledge maps are means to show ideas and concepts connected with a topic, in a well-structured form.

This paper provides an introduction and analysis of the undergoing curriculum reform in China s elementary mathematics education. The curriculum reform is expected to bring a promising future to China s elementary mathematics education.

A few computer based activities aiming to teach mathematical concepts and procedures such as digit value and permutational calculations were developed. In this paper, the guidelines to design such computer assisted activities will be discussed and developed computer based activities will be presented.

The study investigated how six Filipino secondary school mathematics teachers prepared for the task of teaching a beginning college algebra class. Implications for teacher preparation programs and mathematics teacher educators are offered.

This article wants to illustrate the idea of diversity as a chance by seven scenes of concrete classroom situations. In order to find such chances, it is important to realize that students do not only vary in their pace of work and their proficiency level but in many dimensions, e.g., their prior experiences, conceptions, motivations, and strategies.

This paper is an extension of a comparative study on learning style and method preference of students from culturally different parts of the world. The first sample (TMB) was selected from the undergraduate students in the University of Southern Queensland in the Darling Downs region of Queensland in Australia and the second sample (KTM) was selected from the same level of students in Apex College, Kathmandu, Nepal.

The aim of this study is to investigate the role of visualization approach on students conceptual understanding. The results of this study, while there is no statistical difference between the control and experiment groups in terms of procedural learning, experimental group students were more succesful in conceptual learning statistically.

This paper investigates the thoughts of the 8th grade students in Turkey on the mathematics course and the relations between the mathematics courses and other variables such as the students' origins, gender and the mathematics scores students achieved.

The article sustains the idea that the mathematical educations should be performed as a continuous research and discovery, not just as a simple transmission of already known ideas. An essential contribution to this activity would be the invention of new mathematical problems.

On a study that explores four-year elementary education students' understanding of how children learn mathematics through the use of concept maps. Thirteen Canadian and 9 students from Lebanon participated in the study.

On work with fifth grade Latino students, where professors engaged students in cooperative activities while solving mathematical problems. Their work was based upon theories of social interdependence, cognitive development, and behavioral learning.

In this article, an overview of the design and implementation of a development course project of linear algebra is presented. The method of instruction in the project is established upon a cooperative approach, exploration and discovery, and writing.

On investigating the effect of using the Geometer s Sketchpad (GSP) on students understanding of some of the geometrical concepts. The sample consisted of 52 students from the Model School, Yarmouk University, Jordan.

This study discusses how learning experiences with computer-based motion detectors created through innovative professional development activities helped one teacher develop his own ideas about rate of change relative to velocity and position concepts.

This study examines the reasons why four women pursued master degrees in mathematics, in the hopes of shedding light on the question: Why is it that women do not pursue graduate degrees in mathematics to the same degree that men do?

This paper draws on findings from a study conducted in seven primary schools in Seychelles about pupils proficiency in one-step arithmetic word problems to discuss the roles of semantic structures of the problems on the pupils ability to identify the operation required to solve them.

On the outcome of an experiment that attempted to address the language barrier of preparatory year mathematics students, who are acquiring English as a new language of instruction at King Fahd University of Petroleum & Minerals, Saudi Arabia.

On the lessons gleaned from a year-long staff development teacher training experience with urban teachers. The paper addresses the current research on teacher development, describes the implementation of best practices, and shares the results of the year-long study.

On an alternative representation of whole numbers, one that can be constructed as a manipulative model. The material is particularly useful in providing a visual representation of the Greatest Common Divisor and the Least Common Multiple of numbers.

On investigating preservice teachers' views about the value of and purposes for the use of instructional videotapes of teaching and learning situations in mathematics in an elementary mathematics methods course.

On suggesting how an aesthetic image can be added to mathematics education. Calls for reform in mathematics education are premised on shifting teacher attention from an absolutist toward a social constructivist philosophy of mathematics and mathematics education.

On the study investigating the legitmacy of using students' GCE Alternative Ordinary Level Mathematics results to predict their Advanced Level Mathematics results. The study was carried out in Trinidad and Tobago.

On the potential for using concrete examples in helping children to learn mathematics. Specifically here, the use of music and breaking up notes into smaller parts is used as an aid to help children understand abstract fractions.

On the comparison of the teaching of problem-solving and reason in the USA and China. It looks at how problem-solving skills are developed in children and the differences between methods in the two countries.

On the use of ICT software, in this instance a dynamic geometry package, in training future mathematics teachers to be more proficient at using ICT in their mathematics lesson where it is most appropriate.

On how the use of a differentiated problem-solving lesson involving marbles with pre-service and in-service teachers encouraged the development of their own ability to deliver in a differentiated manner to students.

On the possibility of adding an appreciation of the aesthetic nature of mathematics to mathematics education, and the suggestion that the goal of success for all in Mathematics cannot be achieved without providing opportunities for students to experience an aesthetic image of mathematics.

On the extent to which textbooks help to develop children's problem-solving skills, and how under-representation of certain types of addition and subtraction problems in text books affects students' success in these types of question.

Logic is usually left out from education in mathematics. This fact has effects on understanding mathematics and even on learning languages, too. This article sketches the problems and a possible solution.

The authors contend that, moral issues aside, any Lottery can be a useful context for the teaching of some combinatorics, and has an appropriate place in the delivery of the mathematics curriculum.

David Burghes& Peter Galbraith

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